New generalizations of the Reed-Muller codes--I: Primitive codes
IEEE Transactions on Information Theory
On the Number of Points of Some Hypersurfaces in Fnq
Finite Fields and Their Applications
On the second weight of generalized Reed-Muller codes
Designs, Codes and Cryptography
Highest numbers of points of hypersurfaces over finite fields and generalized Reed--Muller codes
Finite Fields and Their Applications
Second weight codewords of generalized Reed-Muller codes
Cryptography and Communications
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For generalized Reed-Muller, GRM(q,d,n), codes, the determination of the second weight is still generally unsolved, it is an open question of Cherdieu and Rolland [J.P. Cherdieu, R. Rolland, On the number of points of some hypersurfaces in F"q^n, Finite Fields Appl. 2 (1996) 214-224]. In order to answer this question, we study some maximal hypersurfaces and we compute the second weight of GRM(q,d,n) codes with the restriction that q=2d.